Thrust nozzles of rocket engines are formed as convergent-divergent expansion nozzles. These nozzles produce optimal thrust when the ambient pressure is of the same magnitude as the average pressure in the nozzle outlet plane. The flow is attached everywhere close to the nozzle wall and does not experience any change of direction at the nozzle outlet in the case of a uniform velocity distribution. If the nozzle outlet pressure is above the ambient pressure, then the gas exit velocity is lower than in the case of the nozzle flow adapted to the ambient pressure. If the nozzle outlet pressure is lower than the ambient pressure, on the other hand, then although the gas exit velocity is higher than in the case of the adjusted nozzle flow, the constriction of the exhaust gas jet that occurs can result in a flow separation. In this case, no separation occurs initially. Only when the pressure at the nozzle end falls to below 40% of the ambient pressure does separation occur. However, once it falls below the ambient pressure, the thrust is no longer optimal.
Flow separations from the wall of the thrust nozzle should be avoided, however, as lateral forces occur that do not act in the desired thrust direction on the rocket engine and can lead to mechanical damage.
The wall contour of the thrust nozzle exerts a substantial influence on the flow progression in the inside of the thrust nozzle and in particular in its divergent section.
Two different contouring methods have basically existed up to now for thrust nozzles, namely a thrust-optimized parabola (TOP) and a so-called truncated ideal nozzle (Truncated Ideal Contour, TIC).
Flow separation and lateral forces occur in principle on start-up of a nozzle, regardless of which type it is. The lateral forces, in particular, can be of different magnitude here depending on the contouring type (TIC or TOP). Normally the aim is to design nozzles in such a way that flow separation is prevented in stationary operation.
Parabolic TOP nozzles generally attain a high nozzle outlet pressure and, if necessary, the nozzle outlet pressure can be increased further by reducing the outlet angle, which is a basic design criterion for avoiding flow separations. At the same time, however, a TOP nozzle produces an internal shock, which can produce a flow separation with subsequent reattachment of the flow to the wall. Especially high lateral forces are generated by this, which can be hazardous for the operation of the rocket engine.
The truncated ideal nozzle (TIC nozzle), on the other hand, is shock-free and prevents the undesirable separation of the flow caused by the particularly high lateral forces arising with subsequent reattachment to the wall. On start-up of a TIC nozzle, only moderate lateral forces therefore occur. However, with the same length of the divergent section of a thrust nozzle and same radius of the end point, a much lower nozzle pressure results with a TIC nozzle than with a TOP nozzle, which leads to the possibility of flow separations occurring in stationary operation with the TIC nozzle.
When designing the nozzle contour of a rocket engine launched on the ground, thus for the rocket engines of the first rocket stage, the unavoidable lateral forces during the start-up should be kept as small as possible, which can be achieved by suppressing the internal shock, so that a flow separation with reattachment is prevented.
A flow separation in stationary operation, meaning on reaching full combustion chamber pressure, should be avoided and in addition the highest possible specific vacuum impulse should be aimed for in stationary operation. Nozzles currently in existence, thus both TOP nozzles and TIC nozzles, cannot fulfill these design criteria simultaneously.
While the wall contour of parabolic TOP nozzles has the form of a quadratic parabola or a higher-order parabola in longitudinal section, the contour of ideal nozzles (TIC nozzles) cannot be described by simple mathematical functions. A design specification for an ideal TIC nozzle has been previously published in: Frey, Manuel, “Behandlung von Strömungsproblemen in Raketendüsen bei Überexpansion” (Dealing with Flow Problems in Rocket Nozzles in the Event of Overexpansion), dissertation, University of Stuttgart, 2001, pages 22 to 27. According to the design specification for ideal nozzles (TIC nozzles) provided there, ideal nozzles are designed using the method of characteristics.
FIG. 2 shows such a design of an ideal rotationally symmetrical nozzle 100, through which a flow passes in the direction of the arrow P from the convergent nozzle section through the throat section to the divergent nozzle section. For the contour of the wall 103 at the narrowest point of the nozzle 100, the nozzle throat 102, a circular arc 104 with a predetermined radius is assumed as default. However, the predetermined radius can also have the value 0, wherein the wall of the convergent section then passes, forming a point of discontinuity creating the throat, directly into the wall of the divergent section.
From the nozzle throat 102 of the example shown in FIG. 2, expansion waves run towards the nozzle longitudinal axis 101, at which they are reflected. The region K upstream of the so-called characteristic last expansion wave propagation line 106, which proceeds from the last point 105 of the circular arc 104 situated in the divergent nozzle section, is termed “kernel.” Expansion waves occur in this kernel region. In FIG. 2 this is the region between the cross-sectional plane E1 at the narrowest throat diameter and the last expansion wave propagation line 106.
The section 108 of the wall 103 downstream of the last point 105 of the circular arc 104 is curved in such a way towards the nozzle longitudinal axis 101 that the expansion waves reflected by the nozzle longitudinal axis and arriving at the wall 103 are immediately cancelled by the compressing wall contour in the section 108. As a consequence, downstream of the last expansion wave reflection-propagation line 107 of the last expansion wave reflected by the nozzle longitudinal axis 101, a parallel flow prevails, and the flow corresponds to the design state. For this reason, this last expansion wave reflection-propagation line 107 is also termed “design characteristic.” At the wall end point 109 where this last expansion wave reflection-propagation line 107 encounters the wall 103, the outlet plane E2 lies in the cross section of the nozzle.
The overall nozzle contour is already determined by the choice of the divergence angle (tangential angle on the circular arc 104) in the end point 105 of the circular arc 104. At a predetermined state in the combustion chamber, there is precisely one contour that can deflect the kernel flow determined by this end point 105 into a parallel flow, namely the ideal contour. If a chosen wall contour is less curved than the related ideal, expansion waves are reflected by the wall 103 into the flow field. However, if it is more strongly curved, compression waves run from the wall 103 into the flow field.